An interesting alt-timeline I had never considered, prompted by a review in the Spectator of Nadine Akkerman's new biography of Elizabeth Stuart, Elizabeth Stuart: Queen of Hearts (OUP, pp. 640, £20). Elizabeth, for refresher's sake, was the second-eldest child of James I, and his oldest daughter who ended up married off to Frederick V of the Palatinate just in time to help him unwittingly kick off the Thirty Years War. Should Charles have pre-deceased James, Elizabeth would have been next in line for the throne. (Charles and Elizabeth were James' only children to survive into adultood.)
Kate Malby does not develop her thesis any farther than her book review requires:
Not only did Elizabeth Stuart model herself on Elizabeth I, but throughout her life English writers praised her as that queen’s reincarnation. Underscoring this biography is the implication that they were right to do so, and that the Scottish-born princess could have done a far better job of ruling the three kingdoms than her younger brother, Charles I. But she never got the chance.
...Having established her heroine’s identification with Elizabeth I, she also misses a few correspondences which could have strengthen her argument. Observing the politics of the early civil war, Elizabeth Stuart was surely adapting her godmother’s motto when she wrote: ‘I hear all and say nothing.’ And in her family portrait by Gerard van Honthorst, I suspect her decision to have herself shown trampling a figure of Medusa owed something to a Tudor tradition in which Medusa represented Catholicism, crushed by Elizabeth I.
The snarky answer might be that one could hardly do worse in managing Parliament than Charles I did in the 1630's and 40's. And Elizabeth, especially if she really was able to sustain her modelling of her Tudor forebear, would certainly be a more sympathetic sovereign antagonist. She also seems to have been less likely to Laudian excess in her religion -- which may well have avoided the Bishops Wars, if nothing else. The problem is, the political dynamic emerging in the English Parliament in the 17th century had deep and rapidly developing social roots. I'm less sanguine that a clash could have been avoided; but it might well have been delayed and channeled in significantly different ways.
Also, of course, the role of her husband Frederick would be a wild card - a wild card Good Queen Bess never had to deal with.